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2x+9=1-2/3x
We move all terms to the left:
2x+9-(1-2/3x)=0
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
2x-(-2/3x+1)+9=0
We get rid of parentheses
2x+2/3x-1+9=0
We multiply all the terms by the denominator
2x*3x-1*3x+9*3x+2=0
Wy multiply elements
6x^2-3x+27x+2=0
We add all the numbers together, and all the variables
6x^2+24x+2=0
a = 6; b = 24; c = +2;
Δ = b2-4ac
Δ = 242-4·6·2
Δ = 528
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{33}}{2*6}=\frac{-24-4\sqrt{33}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{33}}{2*6}=\frac{-24+4\sqrt{33}}{12} $
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